Tentukan \( \displaystyle \int \limits_{-1}^2 (6x^2+8x) \ dx \).
- 24
- 26
- 28
- 30
- 32
Pembahasan:
Ingat bahwa \( \int ax^n dx = \frac{a}{n+1}x^{n+1}+C \) sehingga:
\begin{aligned} \int_{-1}^2 (6x^2+8x) \ dx &= \left[ \frac{6}{3}x^3+\frac{8}{2}x^2 \right]_{-1}^2 \\[8pt] &= \left[ 2x^3+4x^2 \right]_{-1}^2 \\[8pt] &= \left[ 2 \cdot 2^3 + 4 \cdot 2^2 \right]- \left[ 2 \cdot (-1)^3+4(-1)^2 \right] \\[8pt] &= 32-2 \\[8pt] &= 30 \end{aligned}
Jawaban D.